This invention relates generally to drawing with a computer and, more specifically to drawing a smoothly shaped, non-circular, curve by blending a plurality of circular arcs.
There are many computer programs available for generating complex shapes; however, if a user wants to generate a particular smoothly shaped, non-circular, figure such as a heart or other similar figures it is difficult to generate such a smoothly shaped, non-circular, curve from existing programs. The present invention provides a method for forming a smoothly shaped, non-circular, curve by generation of multiple circular arcs that are blended together with each of the circular arcs extending through two points and each of the arcs positioned such that the arcs have a common tangent at a common consecutive point.
In the present invention, a smoothly shaped, non-circular, curve is generated by forming a series of separate circular arcs which adhere to a predetermined pattern. That is, to form a smoothly shaped, non-circular, curve, a first circular arc is drawn that passes through two points, is tangent to a first directed tangent line, and is in the direction indicated by the first directed tangent line. Similarly, a second circular arc is drawn that is tangent to the first arc at one of the aforementioned points and passes through a third point to form a smoothly shaped, non-circular, curve comprised of the first circular arc and the second circular arc with a common tangent. Similarly, for more complex curves, a greater number of circular arcs can be connected together.
Briefly, the present invention comprises a method of generating a smoothly shaped, non-circular, curve, by the formation of multiple circular arcs with common tangents. In the method, one draws a first circular arc which passes through two points and is tangent to a first line extending from a first point in a direction indicated by the line. Next, one repeats the process by drawing a second circular arc which passes through one of the aforementioned two points and a third point and has a common tangent with the first arc at the common point. By utilizing a common point with a common tangent for each of the two circular arcs, one can generate a smoothly shaped, non-circular, curve from the blending of the two circular arcs.